CN110134137B - Spacecraft attitude tracking control method based on extended state observer - Google Patents

Spacecraft attitude tracking control method based on extended state observer Download PDF

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CN110134137B
CN110134137B CN201910527054.6A CN201910527054A CN110134137B CN 110134137 B CN110134137 B CN 110134137B CN 201910527054 A CN201910527054 A CN 201910527054A CN 110134137 B CN110134137 B CN 110134137B
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spacecraft
extended state
state observer
attitude tracking
attitude
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CN110134137A (en
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吴雨瑶
张颖
吴爱国
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Shenzhen Graduate School Harbin Institute of Technology
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Abstract

The invention provides a spacecraft attitude tracking control method based on an extended state observer, which comprises the following steps: s1, establishing a mathematical model of the spacecraft; s2, establishing an error mathematical model of the spacecraft; s3, designing an extended state observer, and estimating the uncertainty of the rotational inertia parameters existing in the spacecraft attitude tracking control and the sum of the uncertainty of the rotational inertia parameters and the external environment interference by the extended state observer; s4, designing an attitude tracking controller based on the extended state observer by utilizing a back stepping method, and taking signals of the extended state observer as compensation signals of the uncertainty of the rotating inertia parameters and the total moment interfered by the external environment in the attitude tracking controller to perform attitude tracking control of the spacecraft. The invention has the beneficial effects that: the method is favorable for grasping each state variable; the controller is more robust, and the accuracy and precision of the control system are improved.

Description

Spacecraft attitude tracking control method based on extended state observer
Technical Field
The invention relates to a spacecraft, in particular to a spacecraft attitude tracking control method based on an extended state observer.
Background
In the problem of attitude tracking of the rigid-body spacecraft, the uncertainty of the existing rotational inertia parameters and the external interference moment received by the spacecraft in the operation process influence the control of the spacecraft to a great extent, and the accuracy and precision of the spacecraft control are reduced.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a spacecraft attitude tracking control method based on an extended state observer.
The invention provides a spacecraft attitude tracking control method based on an extended state observer, which comprises the following steps:
s1, establishing a mathematical model of the spacecraft;
s2, establishing an error mathematical model of the spacecraft;
s3, designing an extended state observer, and estimating the uncertainty of the rotational inertia parameters existing in the spacecraft attitude tracking control and the sum of the uncertainty of the rotational inertia parameters and the external environment interference by the extended state observer;
s4, designing an attitude tracking controller based on the extended state observer by utilizing a back stepping method, and taking signals of the extended state observer as compensation signals of the uncertainty of the rotating inertia parameters and the total moment interfered by the external environment in the attitude tracking controller to perform attitude tracking control of the spacecraft.
As a further improvement of the present invention, step S1 includes:
the kinematic equation and the kinetic equation of the tracking spacecraft based on the modified Reed-Solomon parameter are established as follows:
Figure GDA0003308330540000021
wherein the content of the first and second substances,
Figure GDA0003308330540000022
in order to track the attitude angular velocity of the spacecraft,
Figure GDA0003308330540000023
to track the attitude description of a spacecraft relative to the inertial space, σ×For the oblique symmetric array, the following is defined:
Figure GDA0003308330540000024
m (σ) satisfies
Figure GDA0003308330540000025
J is a system rotational inertia matrix, is a symmetric matrix and meets the requirement
J＝J0+△J
Wherein, J0For a constant symmetric matrix, Δ J is the uncertainty present in the moment of inertia.
The kinematic model of the target spacecraft is as follows:
Figure GDA0003308330540000026
wherein omegadFor a given target attitude angular velocity, σdIs the attitude variable of the target spacecraft.
As a further improvement of the present invention, step S2 includes:
the error kinematic equation and the error kinetic equation are established as follows:
Figure GDA0003308330540000031
wherein σeIs the attitude variable of the error system, omega is the angular speed of the error, and meets the condition that omega is omega-C omegadIn the formula
Figure GDA0003308330540000032
As a further improvement of the present invention, step S3 includes:
the f is all terms containing uncertainty in an error system and meets the requirement
Figure GDA0003308330540000033
Definition of z1、z2Respectively is an observationTwo outputs of the device; let x be ω + K σeWherein K ═ diag (K)1,k2,k3) Is a positive definite symmetric matrix, then x1＝x,x2F is two inputs of the observer; the output error of the observer is e1,e2The form is as follows:
Figure GDA0003308330540000034
the extended state observer was designed as follows:
Figure GDA0003308330540000041
wherein, beta1,β2>0 is an adjustable parameter, and F is defined as follows:
Figure GDA0003308330540000042
as a further improvement of the present invention, step S4 includes:
the designed attitude tracking controller based on the extended state observer is as follows:
Figure GDA0003308330540000043
wherein, b1,b2,b3>0 is an adjustable parameter.
As a further improvement of the present invention, step S4 includes the following sub-steps:
Step 401
considering ω as a virtual control input, the kinematic controller is designed:
α＝-Kσe
wherein K ═ diag (K)1,k2,k3) And there is a constant k min k i1,2, 3. Selecting a Lyapunov candidate function:
Figure GDA0003308330540000044
in the formula, b1For adjustable parameters greater than 0, for V1Derivative to obtain
Figure GDA0003308330540000051
As is apparent from the formula (3), σ is represented by time t → ∞e→0，
Step 402 defines a new error variable x:
x＝ω-α＝ω+Kσe (4)
the error kinetic equation is written as
Figure GDA0003308330540000052
Notes F, G and
Figure GDA0003308330540000053
are respectively of the formula
Figure GDA0003308330540000054
Figure GDA0003308330540000055
Figure GDA0003308330540000056
Order to
Figure GDA0003308330540000057
Then the simplified equation (5) is written as
Figure GDA0003308330540000058
Consider a new Lyapunov candidate function V2The form is as follows:
Figure GDA0003308330540000059
to V2Taking the derivative to obtain
Figure GDA0003308330540000061
If the control law is
Figure GDA0003308330540000062
In the formula, b2For an adjustable parameter greater than 0, then
Figure GDA0003308330540000063
The attitude tracking controller designed by Step 403 based on the extended state observer is
Figure GDA0003308330540000064
Wherein, b1,b2,b3>0 is an adjustable parameter.
As a further improvement of the invention, the parameter of the attitude tracking controller based on the extended state observer is b1＝35,b2＝1,b3＝1000,K＝diag(0.01,0.01,0.01),β1＝20,β2＝300。
The invention has the beneficial effects that:
1. the spacecraft attitude tracking controller based on the extended state observer can enable the closed-loop system under the action of the controller to be globally asymptotically bounded and stable;
2. the extended state observer used in the design of the invention can observe the total disturbance moment f of the uncertainty of the moment of inertia and the external disturbance moment, and inputs the estimated value into the control system as a compensation signal, which is beneficial to the grasp of each state variable;
3. the controller designed by the invention does not need to know the specific value of the interference upper bound in advance, the controller has more robustness, and compared with some existing methods, the controller reduces a large amount of matrix inversion calculation, reduces the calculation burden of an observer, and improves the accuracy and precision of a control system.
Drawings
FIG. 1 is a control system block diagram of a spacecraft attitude tracking control method based on an extended state observer.
FIG. 2 is a system simulation diagram of the spacecraft attitude tracking control method based on the extended state observer.
FIG. 3 is an error angular velocity simulation diagram of the spacecraft attitude tracking control method based on the extended state observer.
FIG. 4 is an error attitude variable simulation diagram of the spacecraft attitude tracking control method based on the extended state observer.
FIG. 5 is a control moment simulation diagram of the spacecraft attitude tracking control method based on the extended state observer.
Fig. 6 is a tracking angular velocity simulation diagram for tracking the angular velocity of the spacecraft, based on the spacecraft attitude tracking control method of the extended state observer of the present invention.
FIG. 7 is a simulation diagram of the total disturbance torque and the estimated value thereof of the spacecraft attitude tracking control method based on the extended state observer.
FIG. 8 shows an extended state observer z of the spacecraft attitude tracking control method based on the extended state observer of the present invention1The estimated error of (1) is simulated.
FIG. 9 is a diagram of the present invention based on dilationExtended state observer z of spacecraft attitude tracking control method of state observer2The estimated error of (1) is simulated.
Detailed Description
The invention is further described with reference to the following description and embodiments in conjunction with the accompanying drawings.
As shown in fig. 1, a spacecraft attitude tracking control method based on an extended state observer includes the following steps:
s1, establishing a mathematical model of the spacecraft;
s2, establishing an error mathematical model of the spacecraft;
s3, designing an extended state observer, and estimating the uncertainty of the rotational inertia parameters existing in the spacecraft attitude tracking control and the sum of the uncertainty of the rotational inertia parameters and the external environment interference by the extended state observer;
and S4, designing an attitude tracking controller based on the extended state observer by using a back stepping method, and using the signal of the extended state observer as a compensation signal of the attitude tracking controller to perform attitude tracking control of the spacecraft.
The method uses modified Reed-Solomon parameters (MRPs) to describe a spacecraft attitude tracking model, takes uncertain items existing in the rotational inertia and external interference as total interference, observes the total interference by using an extended state observer, and takes signals of the observer as compensation signals of a control system to carry out attitude tracking control.
The kinematic equation and the kinetic equation of the tracking spacecraft based on the modified Reed-Solomon parameters (MRPs) are established as follows:
Figure GDA0003308330540000081
wherein the content of the first and second substances,
Figure GDA0003308330540000091
in order to track the attitude angular velocity of the spacecraft,
Figure GDA0003308330540000092
for tracking spacecraft phasesFor attitude description in inertial space, σ×For the oblique symmetric array, the following is defined:
Figure GDA0003308330540000093
m (σ) satisfies
Figure GDA0003308330540000094
J is a system rotational inertia matrix, is a symmetric matrix and meets the requirement
J＝J0+△J
Wherein, J0For a constant symmetric matrix, Δ J is the uncertainty present in the moment of inertia.
The kinematic model of the target spacecraft is as follows:
Figure GDA0003308330540000095
wherein omegadFor a given target attitude angular velocity, σdIs the attitude variable of the target spacecraft.
The error kinematic equation and the error kinetic equation are established as follows:
Figure GDA0003308330540000096
wherein σeIs the attitude variable of the error system, omega is the angular speed of the error, and meets the condition that omega is omega-C omegadIn the formula
Figure GDA0003308330540000101
Designing the controller by using a reverse step method:
Step 1
considering ω as a virtual control input, the kinematic controller is designed:
α＝-Kσe
wherein K ═ diag (K)1,k2,k3) And there is a constant k min k i1,2, 3. Selecting a Lyapunov candidate function:
Figure GDA0003308330540000102
in the formula, b1Is an adjustable parameter greater than 0. Now in pair V1Derivative to obtain
Figure GDA0003308330540000103
As is apparent from the formula (3), σ is represented by time t → ∞e→0。
Step2 defines a new error variable x:
x＝ω-α＝ω+Kσe (4)
the error dynamics equation can be written as
Figure GDA0003308330540000104
Notes F, G and
Figure GDA0003308330540000105
are respectively of the formula
Figure GDA0003308330540000106
Figure GDA0003308330540000111
Figure GDA0003308330540000112
Order to
Figure GDA0003308330540000113
Then the simplified equation (5) is written as
The simplified equation (5) can be written as
Figure GDA0003308330540000114
Consider a new Lyapunov candidate function V2The form is as follows:
Figure GDA0003308330540000115
to V2Taking the derivative to obtain
Figure GDA0003308330540000116
If the control law is
Figure GDA0003308330540000117
In the formula, b2Is an adjustable parameter greater than 0. Then there is
Figure GDA0003308330540000118
It is clear that the control law u contains parameter uncertainties and external disturbance torques, so that it is practically impossible to implement this control law. Therefore, an observer is required to estimate these state variables that are not directly measurable, and the estimated signals are used as compensation signals in the control system.
Step3 designs an extended state observer with f as an extended state variable. Definition of z1、z2Separately divide the two outputs of the observer, x1＝x,x2F is two inputs of the observer; the output error of the observer is
Figure GDA0003308330540000121
The extended state observer was designed as follows:
Figure GDA0003308330540000122
wherein, beta1,β2>0 is an adjustable parameter. Then the achievable control law is
Figure GDA0003308330540000123
Wherein, b1,b2,b3>0 is an adjustable parameter.
Considering the Lyapunov candidate function V3The form is as follows:
Figure GDA0003308330540000124
to V3Taking the derivative to obtain
Figure GDA0003308330540000125
Due to the fact that
Figure GDA0003308330540000131
Then equation (15) can be written as
Figure GDA0003308330540000132
Wherein the content of the first and second substances,
Figure GDA0003308330540000133
the preparation method is easy to obtain,
Figure GDA0003308330540000134
converge on the set D
Figure GDA0003308330540000135
The simulation parameters of the rigid body spacecraft are selected as follows:
nominal value of moment of inertia J is
Figure GDA0003308330540000136
Uncertainty term Δ J of
△J＝diag(sin(0.1t),2sin(0.2t),3sin(0.3t))kg·m2
The interference signal d (t) is
Figure GDA0003308330540000137
Selecting the initial value of the angular speed of the tracked spacecraft to be … (0) < 000]Trad/s, initial value of attitude variable σ (0) [ -0.1579,0.1368, -0.0947]TThe initial attitude variable of the target spacecraft is sigmad(0)＝[0,0,0]T. The initial state of the observer is zi＝[0.01,0.01,0.01]TAnd i is 1 and 2. Target angular velocity is set to
Figure GDA0003308330540000141
In consideration of the practical problem, the magnitude of the control torque provided by the spacecraft actuator is limited, and it is assumed that the magnitude of the control torque provided by the spacecraft actuator is 5N at most. Selecting a parameter of an extended state observer-based attitude tracking controller as
b1＝35,b2＝1,b3＝1000,K＝diag(0.01,0.01,0.01),β1＝20,β2＝300
Fig. 2-9 are simulation diagrams.
The invention provides a spacecraft attitude tracking control method based on an extended state observer, which designs a robust controller based on the extended state observer aiming at the attitude tracking problem of a spacecraft, assumes that the spacecraft is a rigid body spacecraft without a flexible attachment, and introduces the extended state observer to estimate the sum of uncertainty and external interference aiming at the problems of uncertainty of rotational inertia parameters and interference of external environment in the spacecraft attitude tracking control. A spacecraft attitude tracking controller based on an extended state observer is designed by utilizing a back stepping method. And finally, verifying the effectiveness of the designed control algorithm by a simulation example.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (5)

1. A spacecraft attitude tracking control method based on an extended state observer is characterized by comprising the following steps:
s1, establishing a mathematical model of the spacecraft;
s2, establishing an error mathematical model of the spacecraft;
s3, designing an extended state observer, and estimating the uncertainty of the rotational inertia parameters existing in the spacecraft attitude tracking control and the sum of the uncertainty of the rotational inertia parameters and the external environment interference by the extended state observer;
s4, designing an attitude tracking controller based on the extended state observer by utilizing a back stepping method, and taking signals of the extended state observer as compensation signals of the uncertainty of the rotating inertia parameters and the total moment interfered by the external environment in the attitude tracking controller to carry out attitude tracking control on the spacecraft;
step S1 includes:
the kinematic equation and the kinetic equation of the tracking spacecraft based on the modified Reed-Solomon parameter are established as follows:
Figure FDA0003308330530000011
wherein the content of the first and second substances,
Figure FDA0003308330530000012
in order to track the attitude angular velocity of the spacecraft,
Figure 1
Figure FDA0003308330530000013
to track the attitude description of a spacecraft relative to the inertial space, σ×For the oblique symmetric array, the following is defined:
Figure FDA0003308330530000014
m (σ) satisfies
Figure FDA0003308330530000021
J is a system rotational inertia matrix, is a symmetric matrix and meets the requirement
J＝J0+△J
Wherein, J0Is a constant symmetric matrix, and Δ J is the uncertainty present in the moment of inertia;
the kinematic model of the target spacecraft is as follows:
Figure FDA0003308330530000022
wherein omegadFor a given target attitude angular velocity, σdIs the attitude variable of the target spacecraft;
step S2 includes:
the error kinematic equation and the error kinetic equation are established as follows:
Figure FDA0003308330530000023
wherein σeIs the attitude variable of the error system, omega is the angular speed of the error, and meets the condition that omega is omega-C omegadIn the formula
Figure 3
；
Step S3 includes:
the f is all terms containing uncertainty in an error system and meets the requirement
Figure FDA0003308330530000031
Definition of z1、z2Two outputs of the observer respectively; let x be ω + K σeWherein K ═ diag (K)1,k2,k3) Is a positive definite symmetric matrix, then x1＝x,x2F is two inputs of the observer; the output error of the observer is e1,e2The form is as follows:
Figure FDA0003308330530000032
the extended state observer was designed as follows:
Figure FDA0003308330530000033
wherein, beta1,β2>0 is an adjustable parameter, and F is defined as follows:
Figure FDA0003308330530000034
。
2. the extended state observer-based spacecraft attitude tracking control method of claim 1, wherein: the spacecraft is a rigid body spacecraft without flexible appendages.
3. The extended state observer-based spacecraft attitude tracking control method of claim 1, wherein step S4 includes:
the designed attitude tracking controller based on the extended state observer is as follows:
Figure FDA0003308330530000041
wherein, b1,b2,b3>0 is an adjustable parameter.
4. The extended state observer-based spacecraft attitude tracking control method of claim 2, wherein: step S4 includes the following substeps:
Step 401
considering ω as a virtual control input, the kinematic controller is designed:
α＝-Kσe
wherein K ═ diag (K)1,k2,k3) And there is a constant k min ki1,2,3, selecting a Lyapunov candidate function:
Figure FDA0003308330530000042
in the formula，b1For adjustable parameters greater than 0, for V1Derivative to obtain
Figure FDA0003308330530000043
As is apparent from the formula (3), σ is represented by time t → ∞e→0，
Step 402 defines a new error variable x:
x＝ω-α＝ω+Kσe (4)
the error kinetic equation is written as
Figure FDA0003308330530000044
Wherein F, G and
Figure FDA0003308330530000045
are respectively of the formula
Figure FDA0003308330530000051
Figure FDA0003308330530000052
Figure FDA0003308330530000053
Order to
Figure FDA0003308330530000054
Then the simplified equation (5) is written as
Figure FDA0003308330530000055
Consider a new Lyapunov candidate function V2The form is as follows:
Figure FDA0003308330530000056
to V2Taking the derivative to obtain
Figure FDA0003308330530000057
If the control law is
Figure FDA0003308330530000058
In the formula, b2For an adjustable parameter greater than 0, then
Figure FDA0003308330530000059
The attitude tracking controller designed by Step 403 based on the extended state observer is
Figure FDA00033083305300000510
Wherein, b1,b2,b3>0 is an adjustable parameter.
5. The extended state observer-based spacecraft attitude tracking control method of claim 4, wherein: the parameter of the attitude tracking controller based on the extended state observer is b1＝35,b2＝1,b3＝1000,K＝diag(0.01,0.01,0.01),β1＝20,β2＝300。
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